Abstract: To use the terminal resources more efficiently, this paper considers the berth resource and quay crane resource simultaneously, and establishes a two-stage model for joint scheduling of berths and quay cranes considering berth preference and quay-crane movement frequency. The first-stage model adopts the variable-in-time arrival strategy of the ship. A mixed-integer programming model is developed with the goal of minimizing the sum of ship waiting cost, deviation cost, and delay cost. The second-stage model considers interference constraints of the quay crane, and establishes an integer programming model with the minimum moving frequency of quay cranes. MATLAB is used to design an improved adaptive mutation particle swarm algorithm to solve the model. Compared with CPLEX and the original particle swarm algorithm, the proposed algorithm shows the high performance. In the two-stage model, a berth deviation factor[β]is introduced to express the indirect impact of berth deviation on the ship’s workload, and the impact of[β]changes on the ship’s working conditions is analyzed. It is found that under the circumstance of certain quay crane resources during the planned period, the deviation of the ship from the preferred berth will affect the total work cost, especially when the total work load of all ships is large, the increase of[β]will cause a sharp increase in the total cost. The results show that the model and algorithm are effective in solving the problem of berth-quay crane joint scheduling.

Key words: container terminal, continuous berth allocation, quay crane scheduling, joint optimization, particle swarm optimization

摘要： 为了更高效地利用码头资源，同时考虑泊位资源和岸桥资源，建立了考虑泊位偏好和岸桥移动频数的泊位岸桥联合调度两阶段模型。第一阶段模型采用船舶到港时间可变的到港策略，建立了以船舶等待成本、泊位偏离成本、延迟离港成本之和最小为目标的混合整数规划模型。第二阶段模型考虑了岸桥的干扰约束，建立了以岸桥移动频数最小为目标的整数规划模型。使用MATLAB设计改进的自适应变异粒子群算法对模型进行求解，并将结果与CPLEX和原始粒子群算法的求解结果对比，证明该算法的高性能。在两阶段模型中引入泊位偏离因子[β]来表示泊位偏离对船舶工作量的间接影响，分析[β]变化对船工作情况的影响。发现在计划期内，岸桥资源一定的情况下，船舶偏离偏好泊位会影响总的工作成本，尤其是当所有船舶总工作量较大时，[β]增加会造成总成本的激增。结果表明该模型和算法在解决泊位-岸桥的联合调度问题方面的有效性。

关键词: 集装箱码头, 连续泊位分配, 岸桥调度, 联合调度, 粒子群算法